Field of Invention
The present invention relates to a method for measuring polarization transmission matrices of an optical fiber, belonging to fields of optical fiber measurement and sensors. More particularly, the present invention relates to a method for distributedly measuring polarization transmission matrices of an optical fiber and a system thereof.
Description of Related Arts
Polarization is one of the fundamental properties of light. When the light is transmitted in the fiber, the polarization states of the light are changed by the fiber's own parameters (intrinsic birefringence, polarization mode coupling, polarization mode dispersion, etc.), bending and twisting caused by external environment and stress variation. For optical communication systems, this change in the polarization states will cause adverse effects, such as causing inter-symbol interference in the digital transmission channel, and destroying the orthogonality of the polarization states in the WDM system. Therefore, the measurement of polarization-dependent parameters becomes particularly important.
Rayleigh backscattered light of short-pulses in the optical fiber is used to monitor the polarization changes along the fiber length, and then changes of fiber polarization-related parameters or environmental parameters are obtained. The technology is known as polarization-sensitive optical time-domain reflectometry, wherein the advantages thereof are: being non-destructive, which will not damage the optical fiber, and will not affect forward transmission of light; and single-ended measurement, wherein the light source and the detector are at the same end of the fiber to be tested, so as to provide far end measurement of long distance fibers.
However, the conventional measurement methods have obvious limitations. In particular, most of the methods only obtain birefringent scalars, rather than birefringent vectors. Therefore, the conventional polarization-sensitive optical time-domain reflectometry can only sense a single-position perturbation on the fiber in once measurement, and lacks ability to effectively detect the simultaneous perturbations of multiple points. For detecting the simultaneous perturbations of multiple points, it is necessary to distributedly measure the polarization states in the transmission direction of the optical pulse in the optical fiber, which needs to measure the fiber polarization transmission matrices (i.e., the Mueller matrices) in a distributed way. As far as we know, there is no way to measure the Mueller matrices distributedly.
If a moderate-power single pulse with a short duration (non-linear birefringence is not induced) is input into the fiber, the transmitted polarization state St in the Stokes space can be expressed as:St=M(z)Sin  (1)
wherein Sin represents polarization of light transmitted from point 0; M(z) represents normalized 4×4 polarization transmission matrix (the Mueller matrix) from the input end of the fiber (point 0) to the scattering point (point z) without non-linear birefringence. The polarization state of Rayleigh backscattered light at point z received at point 0 can be expressed as:SB=MsM(z)TMsM(z)Sin  (2)
wherein SB is the polarization state of Rayleigh backscattering light demodulated at point 0; M(z)T represents the transpose of M(z); and Ms can be expressed as:
                              M          s                =                  (                                                    1                                            0                                            0                                            0                                                                    0                                            1                                            0                                            0                                                                    0                                            0                                            1                                            0                                                                    0                                            0                                            0                                                              -                  1                                                              )                                    (        3        )            
For most optical fibers, linear birefringence is dominant in the absence of non-linear birefringence in the fiber. The reason is that circular birefringence can be neglected in most cases because the propagation constant difference between the left-handed and right-handed circular polarizations is very small relative to the two orthogonal linear modes.
The polarization transmission matrices M(z) have some symmetric features. In the presence of linear birefringence only, the polarization transmission matrix of the fiber from the point 0 to point z, namely the Mueller matrix, can be expressed as:
                              M          ⁡                      (            z            )                          =                  (                                                    1                                            0                                            0                                            0                                                                    0                                                                                                                                                                                      cos                            2                                                    ⁢                          2                          ⁢                                                                                                          ⁢                          θ                                                +                                                                                                                                                                          sin                          2                                                ⁢                        2                        ⁢                                                                                                  ⁢                        θ                        ⁢                                                                                                  ⁢                        cos                        ⁢                                                                                                  ⁢                        γ                                                                                                                                                                                                                                      cos                          ⁢                                                                                                          ⁢                          2                          ⁢                                                                                                          ⁢                          θ                          ⁢                                                                                                          ⁢                          sin                          ⁢                                                                                                          ⁢                          2                          ⁢                                                                                                          ⁢                          θ                                                -                                                                                                                                                cos                        ⁢                                                                                                  ⁢                        2                        ⁢                                                                                                  ⁢                        θ                        ⁢                                                                                                  ⁢                        sin                        ⁢                                                                                                  ⁢                        2                        ⁢                                                                                                  ⁢                        θ                        ⁢                                                                                                  ⁢                        cos                        ⁢                                                                                                  ⁢                        γ                                                                                                                                          sin                  ⁢                                                                          ⁢                  γ                  ⁢                                                                          ⁢                  sin                  ⁢                                                                          ⁢                  2                  ⁢                                                                          ⁢                  θ                                                                                    0                                                                                                                                                          sin                          ⁢                                                                                                          ⁢                          2                          ⁢                                                                                                          ⁢                          θ                          ⁢                                                                                                          ⁢                          cos                          ⁢                                                                                                          ⁢                          2                          ⁢                                                                                                          ⁢                          θ                                                -                                                                                                                                                sin                        ⁢                                                                                                  ⁢                        2                        ⁢                                                                                                  ⁢                        θ                        ⁢                                                                                                  ⁢                        cos                        ⁢                                                                                                  ⁢                        2                        ⁢                                                                                                  ⁢                        θ                        ⁢                                                                                                  ⁢                        cos                        ⁢                                                                                                  ⁢                        γ                                                                                                                                                                                    sin                      2                                        ⁢                    2                    ⁢                                                                                  ⁢                    θ                                    +                                                            cos                      2                                        ⁢                    2                    ⁢                                                                                  ⁢                    θ                    ⁢                                                                                  ⁢                    cos                    ⁢                                                                                  ⁢                    γ                                                                                                                    -                    cos                                    ⁢                                                                          ⁢                  2                  ⁢                                                                          ⁢                  θ                  ⁢                                                                          ⁢                  sin                  ⁢                                                                          ⁢                  γ                                                                                    0                                                                                  -                    sin                                    ⁢                                                                          ⁢                  γ                  ⁢                                                                          ⁢                  sin                  ⁢                                                                          ⁢                  2                  ⁢                                                                          ⁢                  θ                                                                              cos                  ⁢                                                                          ⁢                  2                  ⁢                                                                          ⁢                  θ                  ⁢                                                                          ⁢                  sin                  ⁢                                                                          ⁢                  γ                                                                              cos                  ⁢                                                                          ⁢                  γ                                                              )                                    (        4        )            
wherein γ=L|Δβ|=L(|βL|2+|ΔβC|2)1/2, θ is an angle between the fast axis and the x-axis of the reference frame, L is the length of the optical fiber, ΔβL is the linear birefringence, ΔβC is the circular birefringence, and Δβ is the total birefringence. The parameter φ is defined as tan(φ)=|ΔβC|/|ΔβL|, φε[−π/2, π/2]. According to the assumption of the present invention, the propagation constants of the left-handed and the right-handed circular polarizations are equal, i.e. φ=0, so the term related to the parameter φ are omitted in the equation (4).
From the equation (4), symmetric features of the Mueller matrices can be obtained. The element at the second row and the third column equals to the elements of the third row and the second column; the element of the second row and the fourth column is negative to the element of the fourth row and the second column; and the element of the third row and the fourth column is negative to the element of the fourth row and the third column. Due to the symmetric features of the Mueller matrices,MsM(z)TMs=M(z)  (5).
It should be noted that the positive integer powers of the Muller matrices have the same symmetric features and, at the same time, have the same sign distribution as the first power.